CRC 326 - GAUS

Higher algebra
2025-10-23 11:15 - 12:45 (Europe/Berlin) | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 1: From categories to ∞-categories
Marvin Schneider (Universität Heidelberg)

Some cases of cube sum problem
2025-10-24 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
Dipramit Majumdar (IIT Madras / Universität Heidelberg)
Abstract: An integer n is said to be a rational cube sum or simply a cube sum if n can be written as a sum of cubes of two rational numbers. For example, 6 = (17/21)^3+ (37/21)^3. A cube-free integer n > 2 is a cube sum if and only if the elliptic curve y^2=x^3-432n^2 has infinitely many solutions over the rational numbers. A recent result of Alpöge-Bhargava-Shnidman-Burungale-Skinner shows that a positive proportion of integers are cube sums and a positive proportion of integers are not.
We will discuss the cube sum problem for some special family of integers. This talk is based on joint works with De, Jha, Mondal, Shingavekar and Sury.

Seminar on Arithmetic Geometry
2025-10-24 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Michael Rapoport (University Bonn): Toric schemes and integral models of Shimura varieties
The modular curve with Gamma0(p)$-level structure has a beautiful integral model over BZp, and generalizations of this model to any Shimura variety with p-parahoric level have been constructed in the last 30 years. When passing from Gamma0(p)-level to Gamma1(p)-level, the situation changes drastically. In the talk I will explain a general method that potentially allows to deal with such level structures. The method is based on the construction of torus embeddings of the maximal torus of a reductive group scheme. Joint work with G. Pappas.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

Riemann-Hilbert Correspondence in characteristic p
2025-10-27 10:00 - 12:00 | Mainz, Hilbertraum 05-432
Introduction by Tom Bachmann (JGU Mainz)
We will be learning about the Riemann-Hilbert correspondence in characteristic p, relating ètale sheaves and Frobenius modules, following the presentation of Akhil Mathew. The current version of the program can be found at: http://tom-bachmann.com/programm-RH.pdf

Noether-Lefschetz loci in A_g and modularity
2025-10-27 15:15 - 17:45 | Darmstadt
15:15 – 16:15 Riccardo Zuffetti (TU Darmstadt): Introduction to the modularity conjecture
16:45 – 17:45 Mingkuan Zhang (TU Darmstadt): The moduli space of abelian varieties

Konstruktion von Galoisüberlagerungen mithilfe starr-analytischer Verklebung
2025-10-30 09:15 - 10:45 | Heidelberg, MATHEMATIKON, SR 7, INF 205, Heidelberg, 69120, Germany
Talk 3: Proendliche Gruppen
Immanuel Klevesath (Universität Heidelberg)

Higher algebra
2025-10-30 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 2: Basic categorical constructions with ∞-categories
Anna Blanco Cabanillas (Universität Heidelberg)

Riemann-Hilbert correspondence in characteristic p
2025-11-03 10:00 - 12:00 | Mainz, Hilbertraum 05-432
Lorenzo Mantovani (JGU Mainz)
Étale cohomology

International Seminar on Automorphic Forms
2025-11-03 15:00 - 16:00
Talk 1: Modular Heights of Unitary Shimura Varieties
Ziqi Guo (Peking University)
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

Tame Local Langlands
2025-11-04 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 3: Definition of Isoc_G
Michelle Klemt (TU Darmstadt)
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

Konstruktion von Galoisüberlagerungen mithilfe starr-analytischer Verklebung
2025-11-06 09:15 - 10:45 | Heidelberg, MATHEMATIKON, SR 7, INF 205, Heidelberg, 69120, Germany
Talk 4: Verklebung kompatibler Familien von Galoisüberlagerungen
Christian Dahlhausen (Universität Heidelberg)

Higher algebra
2025-11-06 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 3: Interlude: Spectra
Jakob Burgi (Universität Heidelberg)

Seminar on Arithmetic Geometry
2025-11-07 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Fei Ren (Bergische Universität Wuppertal): Coherent Six-Functor Formalisms: Pro vs Solid
In the classical theory for coherent sheaves, the only missing piece in the Grothendieck
six-functor formalism picture is j! for an open immersion j. Towards fixing this gap, Deligne
provided a construction of j! by extending the sheaf class to pro sheaves, while Clausen-
Scholze provided another solution by extending the sheaf class to solid modules.
In this talk, I will explain how Deligne’s construction coincides with the Clausen-Scholze construction via a natural functor, whose restriction to the full subcategory of Mittag-Leffler pro-systems is fully faithful.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

Riemann-Hilbert correspondence in characteristic p
2025-11-10 10:00 - 12:00 | Mainz, Hilbertraum 05-432
Timon Tausendpfund (JGU Mainz)
Prestable and derived categories

Noether-Lefschetz loci in A_g and modularity
2025-11-10 15:15 - 17:45 | Frankfurt am Main
15:15 – 16:15 Nicole Müller (Goethe Universität Frankfurt): The tautological ring of A_g
16:45 – 17:45 Miguel Prado Godoy (Goethe Universität Frankfurt): The toroidal compactification of A_g and its tautological ring

Tame Local Langlands
2025-11-11 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 4: The Newton map
Paul Siemon (TU Darmstadt)
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

International Seminar on Automorphic Forms
2025-11-11 16:00 - 17:00
Twisted period integrals and applications
Zhiyu Zhang (Stanford University)
The Waldspurger formula reveals a striking relation between twisted versions of Hecke periods and central L-values of modular forms. The use of quadratic twists is crucial in many applications, including equidistribution of integer points on spheres and of Heegner points. In this talk, I will present the twisted Gan-Gross-Prasad conjecture on twisted versions of tensor product L-functions. In particular, it provides new information on twisted symmetric square L-functions of modular forms, via the Langlands transfer of quadratic base change. I will outline a proof of this conjecture under some local assumptions, based on joint work with Lu and Wang. There are some essential differences compared to untwisted settings, leading to new applications and new questions.
Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).

p-adic Simpson correspondence
2025-11-12 14:00 - 18:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
Talk 3: Dmytro Rudenko (Leibniz Universität Hannover): Classical 𝑝-adic Hodge-Tate decomposition
Talk 4: Jakob Stix (Goethe Universität Frankfurt): Hodge-Tate spectral sequence for 𝔾𝑚

Konstruktion von Galoisüberlagerungen mithilfe starr-analytischer Verklebung
2025-11-13 09:15 - 10:45
Talk 5: Konstruktion von Keimen analytischer Galoisüberlagerungen
Alberto Merici (Universität Heidelberg)

Higher algebra
2025-11-13 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 und Zoom, Germany
Talk 4: Stable ∞-categories
Nils Witt (Universität Heidelberg)

Riemann-Hilbert correspondence in characteristic p
2025-11-17 10:00 - 12:00 | Mainz, Hilbertraum (05-432)
Niklas Stelzer (JGU Mainz)
Frobenius modules

Tame Local Langlands
2025-11-18 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 5: Geometry of Isoc_G
Zeyu Wang (MIT)
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

The Gross-Zagier formula on singular moduli for Shimura curves
2025-11-18 15:00 - 16:00 | Zoom
International Seminar on Automorphic Forms
Andrew Phillips (College of Idaho): The Gross-Zagier formula on singular moduli for Shimura curves
The Gross-Zagier formula on singular moduli, which gives a formula for the prime factorization of differences of j-values, can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We will discuss a generalization of this result to a Shimura curve.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits)

p-adic Simpson correspondence
2025-11-19 14:00 - 18:00 | Frankfurt, Robert-Mayer-Str. 6-8, Raum 309
Talk 5: Magnus Carlson (Goethe Universität Frankfurt): Rigid analytic groups 1
Talk 6: Ruth Wild (Goethe Universität Frankfurt): Rigid analytic groups 2

Konstruktion von Galoisüberlagerungen mithilfe starr-analytischer Verklebung
2025-11-20 09:15 - 10:45 | Heidelberg, MATHEMATIKON, SR 7, INF 205, Heidelberg, 69120, Germany
Talk 6: Beweis von Theorem 1
Nils Witt (Universität Heidelberg)

Higher algebra
2025-11-20 11:15 - 12:45 | Heidelberg, Mathematikon, SR 8 and Zoom, INF 205, Heidelberg, Germany
Talk 5: Derived ∞-categories
Vincent Zahlen (Universität Heidelberg)

Seminar on Arithmetic Geometry
2025-11-21 15:30 - 17:00 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Ioannis Zachos (University Münster): On integral models for some ramified unitary Shimura varieties
Local models of Shimura varieties are projective flat schemes over the spectrum of a discrete valuation ring. The importance of local models lies in the fact that under some assumptions they model the singularities that arise in the reduction modulo p of Shimura varieties. In this talk, we will first introduce the notion of local models and certain variants of them for some ramified unitary Shimura varieties. Building on this, we will resolve the singularities of these models, leading to regular integral models for the corresponding Shimura varieties. In the end we will discuss the Bruhat-Tits stratification of the associated Rapoport-Zink spaces.
Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)

Riemann-Hilbert correspondence in characteristic p
2025-11-24 10:00 - 12:00 | Mainz, Hilbertraum (05-432)
Georg Tamme (JGU Mainz)
The Breen-Deligne resolution (1)

Tame Local Langlands
2025-11-25 14:00 - 15:30 | Darmstadt, Room 401 and Zoom, Schlossgartenstraße 7, Darmstadt, 64289, Germany
Talk 6: Duality and Trace formalism
Tomás Perutka (University of Münster)
Zoom (612 2072 7363, Password: [REDACTED] six digit prime number)

Refined equidistribution of Hecke points and cryptography
2025-11-25 15:00 - 16:00 | Zoom
International Seminar on Automorphic Forms
Radu Toma ( Institut de mathémathiques de Jussieu): Refined equidistribution of Hecke points and cryptography
A classic theorem states that, fixing a Euclidean lattice L, its sublattices of large index equidistribute in the space of lattices. The literature leaves open the question: how does the rate of equidistribution depend on L? In joint work with de Boer, Page, and Wesolowski, we answer this using automorphic theory and geometry of numbers. Motivated by lattice-based cryptography, we apply the result to show that a computational problem called SIVP is as hard for Haar random module lattices as it is in the worst case.
https://tu-darmstadt.zoom.us/j/68048280736
The password is the first Fourier coefficient of the modular j-function (as digits)
